Electrical wave filter



April 18, 1961 w. H. cox

ELECTRICAL WAVE FILTER Filed Aug. 5, 1957- L LL T L L T L NK-www Fl G. 2.

,4 INVENTOR.

WILLIAM H. COX

ATTORNEYS ELECTRICAL WAVE FILTER William H. Cox, Beaumont, Tex., assignor to Sim Oil Iornpany, Philadelphia, Pa, a corporation of New ersey Filed Aug. 5, 1957, ser. No. 676,080

4 claims. (ci. ass-2s) This invention relates to electrical wave4 filters and has particular reference to filters of the delay line type.

In my application, Serial No. 464,843, filed October 26, 1954, now abandoned, there is described, particularly in connection with the analysis of seismic records, a type of filter in which a Wave is analyzed against apredetermined waveform or wavelet. In brief, in accordance therewith, desired signals are separated from noise on the basis of wave shape or character instead of frequency content only, the filtering being particularly adapted for the detection of transients. In effect, at any instant of time the Waveform undergoing analysis is multiplied by corresponding values of a predetermined wavelet, and integration of the product'is taken over a predetermined time period of the waveform. The integration is most readily carried out in the form of a summation of discrete values of the product of the waveform by the wavelet, and this summation is most readily accomplished by feeding the waveform to be analyzed to a delay line provided with suitably spaced taps-from Which values are taken, each of which is elfectively multiplied by a v-alue corresponding to an ordinate of the j wavelet and the resulting discrete products are then` summed to provide an output. t An actual delay line `is necessarily made up `of components which have finite electrical loss. That is, a signal Vwill be attenuated as it travels down the` delay line.

For proper results, there must be compensation for `this attenuation by an adjustment of the amplitude multiplying factors to provide the desired filter characteristic. This would `ordinarily involve a considerable amount of calculation, particularly if the shape lof `the wavelet involved in the analysis is changed. The present invention relates-particularly to compensation` forl- Vthe attenuation and'involves a relatively -simple arrangement of resistors particularly in View 4of the fact thatl the wavelet patterns ordinarilyof significance are symmetrical, kcorresponding. to symmetry of the. multiplyingsfactorswith respect tothe center of the delay ,line. Symmetry is particularly desired'te 'eliminate phase distortion ofthe signal. Vf lf, then,` the ordinate patterns are, limited `to theclass .ofsymmetrical ,ones, `an ordinate pairing circuit-may be vused ito simplify the procedureof changing filter proper ties. Line loss` compensation and pairingaofwsymmetrical ordinates may be built Vinto a fixed part of thecircuit.

Only one additional amplitude adjustment per ordinate pair-sAthen-needed torobtain any symmetrical Vordinate effect isequivalent `to producing, substantially/fan output of-Wavelet filtering yconnection with the'analysis ing is of more general applicability particularly for the detection of transients of predetermined waveform in any type of wave or record.

The general object of the invention is the provision of means in such a filtering arrangement adapted to compensate for delay line losses. Other objects of the invention will become more apparent from the following description, read in conjunction with the accompanying drawing, in which:

Figure 1 is a wiring diagram showing in association with; a delay line of a wavelet filter the particular means torwhich the present invention relates; and

Figure 2 shows certain formulae which are involved in calculations in accordance ywith the invention, and areV explanatory thereof.

Referring first to Figure 1, there is indicated at 2 a delay -line to which there is fed the waveform undergoing analysis. This line may be of many typeswell known in the art, but for simplicity of illustration it is shown as having sections each of which is grounded at 4 and tapped at 6 between sections, the sections being pi sections provided by inductances 8 and capacitances 10. Other known types of delay lines may be used. The input terminals of the line are indicated at l2 and the output terminals indicated at 14. As illustrated, the delay line is symmetrical about the center tap 6 to which there is connected the resistor 16 leadingto a terminal 18 connected to ground through a resistor 2i) having the same resistance value `as resistor 16. Pairs of taps symmetrically disposed about. the center tap 6' are connected through resistors 22 to terminals 24, each of the latter of which then corresponds to a symmetrically located pair of taps 6. The invention particularlyrelates to the provision of `resistors 22 which compensate for the loss` characteristics of the line. As shown in Figure l, the terminal 18 is connected to a terminal 26', and each of the terminals 24 is connected to a corresponding terminal 26. v `These latter xterminals maybe constituted by plugs receivable in sockets which are connected, as will be presently described, .to other parts of the apparatus. The system is such that =at the terminals 26 and 26 signals are delivered having such relative amplitude as to correspond substantially to a loss-less delayline. The as sembly comprising thel delay line and resistors 16 and 22 and their corresponding terminals 'may provide a unit which Vneed not be changed if the reference wavelet is changed. VIn other words, once the resistors i6 and 22 are ydetermined in value, the outputs from theterminals 26 and '26" may be quite arbitrarily treated Without change of the delay line assembly. Furthermore, the wavelet-characterizing devices connected to these output terminals need not be `calculated in the light of the loss -aTof each of the terminals` 26 and 261v there is connected the resistance of a'potentiometer 28;V the opposite terminal of each of these being groundedas indicated at 30. The contacts of these potentiometers are adjusted in ac Y cordance with the wavelet involved in the ltering and are Vvror'n am ideal vdelayY line involving norlosrs, dej/ration from f anideal; line being So[slightlas-'toghe` ydegli'gilbljefin lVllhilenny prior .application- .particularly relates 4to the connected through adding resistors 32 to one `or the other of a: pair'zof lines 34 andf 36 which deliver anoutput through a transformer 38the center tap of the primary ofY which is grounded as indicated at 40. The 'linesj34 Vand .36 vrespectively correspond to assignment `of positive and negative'values to the inputs theretoand,-as shown, are connectedto the end terminals of theprimary of trans-` former 3 8, fForreferencethey are respectively designated by v.the-plus signfor apnsitive assignment of`value and 'nus sign f ""a negatveassignment of value1 (These fg'of 'cours'erdo notV indicate direct current relation-y Patented Apr. l, 1961 ships in this instance.) The ratio of resistance values of the potentiometers provided'between their adjustable contacts and ground to the total (equal) resistances of the potentinnetesV correspond to ordinatesV of the reference' wavelet. As illustrated, the wavelet may be considered as having at its center of time symmetry Ka'maximum positive.

ordinate with the ordinates remaining positive through the third ordinate, the fourth, fifth, sixth and seventh ordinates being negative, with the wavelet then going positive and running to a low value at the end ordinates illus# trated. It will be noted that the'connections are to the positive line 34 when the ordinates are positive andv to the negative line 36 when they are negative.

The resistors 32 may be of high equal vide for the separate summing of the respective inputs to the lines 34 and`36.

While a simple arrangement is illustrated,l involving re-l sistors only, it may be desirable, if very highjaccuracy is desired, to interpose in the connections isolating means such as cathode followers, but such isolating means are not generally necessary for accuracies required in practice.

The operation is such that if the delay line were assumed loss-less, there would be delivered to each of theV terminals 26 a signal corresponding to one-halfV the sum of the signals appearing at the delay line taps connected through a pair of resistors 22 to such terminals. Actually, this is the effect achieved as will become justiiied hereafter. The signal thus appearing at a terminal 26 is effectively multiplied, by reason of voltage division at the potentiometers 28, by a value corresponding to awavelet ordinate, the multiplication factor being the ratio of the vpotentiometer resistance between the potentiometer contact and ground to the total resistance of the potentiometer.V These individual products are then added through resistors 32 and delivered to the respective. lines 34 and 36. In view of the factor of one-half which is introduced,

the arf stantially loss-less delay line and the attainmentV of the same impedance at each-terminal 26. The samev source impedance, of course, must be presented by each terminal factor for each pair of taps introduced by the relative values of the constant resistances of the potentiometers 28 and the constant source resistances appearing at the terminals 26 and 26', the last being as hereafter described. In the calculations this factor drops out.) These results follow from conventional delay line theory. If the delay line were loss-less, u would be 0, and for E1 to be equal to E2, R1 would be'equal to R2; In the case of the actual line it is desired to have E1 equal to E2, and R1 and R2 must be relatively chosen to secure this equality. By equating E1 to E2, and solving for the ratio of R1 to R3, Equation 3 is obtained.

It will be noted that lthis equation ldoes not give definite valuesto the resistances but onlytheir ratios. It is now desired to provide at every terminal 26 the same impedance looking toward the delay line, and this impedance should be that appearing, looking toward the delay line, at terminal 26'. VEquationV 4 represents this requirement, neglecting the negligible contribution to the impedance due to the source impedance of the delay line itself and the source feeding the delay line, the delay line inductors and source being chosen to exhibit resistances Very small in comparison with the values of resistors 22. R0 is the desired impedance. By the simultaneous solution of Equations 3 'and 4, there are obtained the values R1 and R2 given in Equations 5 and `6, for the respective resistances 22 of each pair. These values, it will be noted, are in terms of the desired impedance, the given attenuation of each filter section, and the spacing, in terms of number of filter sections,'between taps under consideration and the center tap'of they line.

t It may here be noted that while for a corresponding pair of taps E1 and E2' are e'qual,these values are not,

. strictly speaking, the sameV as those for pairs of taps differently spaced from the center tap. In fact, derived from the foregoing, El and'E'zj are as specifiedl in Equa- Vtion 7 in Figure 2. However, the attenuation constant erally closely approximate .one-half for all tapsV of the filter. If the very small correction involved in'Equation 7 is to be taken into account, that may be done in the setting of adjustments of the potentiometers. For most purposes, Vsuch as those involved in seismic-wave analysis, such correction is unnecessary. It will be noted p that .the potentialrappearing at terminal 26, is E/Z.

26 to the adjustable part of thecircuit Vinvolving the potentiometers 28. v Y It will suce vto consider asingle pair of taps 6 sym metrically related to the center tap 6.

The subscript 0 appended to a term relates to the center tap 6';` the sub-Y script l refers to the tap 6 under consideration which lies onr the input side of the center tap; and the subscript 2 relates to the terminal 6 under,k oonsideration'which lies"V form onthe Vdelay'line as it vappears at terminal 6', then l the. samelinstantaneous Yvalue of the waveformwhen it appears at thertaps under consideration will produce, as

r'neasuredj-at the corresponding terminal 26, equivalent internal voltagesat thesource which are jE! andnEg given ',Fig'ure: 2j. ,(Tliejse From the foregoing it will be evident that when the resistors 22 are chosen in accordance with the foregoing, the delay line assembly as it appears at the terminals 26 andV 26 is, eiectively, a loss-less line.v Accordingly, once Ythis arrangement is set up,Y there is no used for providing, in ,eiect, a substantially loss-less deabove.

`of simple setting of lay line if,an odd number of sections are used.` Symmetry of the delay line and of the reference wavelet leads, in accordance with-the invention, to the possibility the vIsotentriometers as described what is claimed is:

1. In combination, a rdelay line comprising `sections connected at taps, said delay line being of a type to provide delay of signals introduced thereto 'without substan- 'I tial distortion of thewave shape thereof, and said delay line being symmetrical with respect to its center, a terminal corresponding to'each pair oftaps disposed symmetricallywith respect to thecenter of .the delay line,

, andiresistors`connecting`each of -saidterminals with the two taps, andonly to the twotaps, t'o which'it corresponda-saidresistors constituting meansY forsubstantially compensatiug 'for attenuation in 4the delay line so that thebutput "signal components at eachv terminal originating at its corresponding taps are substantially equal for a given'event of a wave traversing the delay line, and an adjustable voltage divider connected to each of said terminals and receiving signals therefrom.

2. In combination, a delay line comprising sections connected at taps, said delay line being of a type to provide delay of signals introduced thereto without substantial distortion of the wave shape thereof, and said delay line being symmetrical with respect toV its center, a terminal corresponding to each pair of taps disposed symmetrically with respect to the center of the delay line, and resistors connecting each of said terminals with the two taps, and only to the two taps, to which it corresponds, said resistors constituting means for substantially compensating for attenuation in the delay line so that the output signal components at each terminal originating at its corresponding taps are substantially equal for a given event of a wave traversing the delay line, and for providing that the input impedances at said terminals are substantially equal, and an adjustable voltage divider connected to each of said terminals and receiving signals therefrom.`

`3. In combination, a delay line comprising sections connected at taps, said delay line being of a type to provide delay of signals introduced thereto without substantial distortion of the wave shape thereof, and said delay line being symmetrical with respecty to its center, a terminal corresponding to each pair of taps disposed symmetrically with respect to the center of the delay line, resistors connecting each of said terminals with the two taps, and only to the two taps, to which it corresponds, said resistors constituting means for substantially compensating for attenuation in the delay line so that the output signal components at each terminal originating at its corresponding taps are substantially equal for a given event of a wave traversing the delay line, an adinstable voltage divider connected to each of said terminals and receiving signals therefrom and having an output connection, and a pair of lines connected by adding resistors to the output connections of said voltage dividers.

4. In combination, a delay line comprising sections connected at taps, said delay line being of a type to provide delay of signals introduced thereto without substantial distortion of the wave shape thereof, and said delay line being symmetrical with respect to its center, a terminal corresponding to each pair of taps disposed symmetrically with respect to the center of the delay line, and resistors connecting each of said terminals with the two taps, and only to the two taps, to which it corresponds, said resistors constituting means for substantially compensating for attenuation in the delay line so that the output signal components at each terminal originating at its corresponding taps are substantially equal for a given event of a wave traversing the delay line, and for providing that the input impedances at said terminals are substantially equal, an adjustable voltage divider connected to each of said terminals and receiving signals therefrom and having an output connection, and a pair of lines connected by adding resistors to the output connections of said voltage dividers.

References Cited in the tile of this patent UNITED STATES PATENTS Pfleger June 29, 1948 2,743,367 Felch et al. Apr. 24, 1956 2,759,044 Oliver Aug. 14, 1956 2,760,164 Graham et al. Aug. 2l, 1956 OTHER REFERENCES Corrington et al.: RCA Review, vol. 15, No. 2, June 1954, pages 163-186. 

